Unlikely.
Firstly what you copy from a tutorial is just text. To automatically run it on paste the text needs to contain a carriage return. It doesn't, so the utility needs to add it. If it's done automatically, it will affect every piece of text you copy, not only shell commands - how'd it tell the difference?
Secondly you'd need to link the browser process and the shell process together in a way that events in one directly affect the other. Check ps -ef
when your Firefox is running - how to identify the appropriate process to link? How about if you have multiple shell instances running - how would the appropriate process be identified?
Most important are however the severe security implications user1686 brought up in his comment.